A linear regression line is of the form w

_{1}x+w

_{2}=y and it is the line that minimizes the sum of the squares of the distance from each data point to the line. So, given n pairs of data (x

_{i}, y

_{i}), the parameters that we are looking for are w

_{1}and w

_{2}which minimize the error

and we can compute the parameter vector

**w**= (w

_{1}, w

_{2})

^{T}as the least-squares solution of the following over-determined system

Let's use numpy to compute the regression line:

from numpy import arange,array,ones,random,linalg from pylab import plot,show xi = arange(0,9) A = array([ xi, ones(9)]) # linearly generated sequence y = [19, 20, 20.5, 21.5, 22, 23, 23, 25.5, 24] w = linalg.lstsq(A.T,y)[0] # obtaining the parameters # plotting the line line = w[0]*xi+w[1] # regression line plot(xi,line,'r-',xi,y,'o') show()We can see the result in the plot below.

You can find more about data fitting using numpy in the following posts:

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